Boundary layer response to arbitrary accelerating flow

Abstract:

This thesis was aimed developing a fundamental understanding of the boundary layer response
to arbitrary motion. In this context arbitrary motion was defined as the unsteady translation and
rotation of an object.
Research objectives were developed from the gaps in knowledge as defined during the literature survey.
The objectives were divided into three main activities; mathematical formulations for non-inertial
bulk flow and boundary layer equations, implementation of said formulations in a numerical solver and
simulations for various applications in arbitrary motion.
Mathematical formulations were developed for the bulk flow and boundary layer equations in arbitrary
motion. It was shown that the conservation of momentum and energy equations remains invariant
in the non-inertial forms. The conservations of momentum equation can at most have six fictitious terms
for unsteady arbitrary motion. The origin of the terms were found to be from transformation of the material
derivative to the non-inertial frame. All fictitious terms were found to be present in the boundary
layer equations, none could be eliminated during an order of magnitude analysis.
The vector form of the non-inertial equations were implemented in a novel OpenFOAM solver. The
non-inertial solver requires prescribed motion input and operate on a stationary mesh. Validation of the
solver was done using analytical solutions of a steady, laminar flat plate and rotating disk respectively.
Numerical simulation were done for laminar flow on a translating plate, rotating disk and rotating
cone in axial flow. A test matrix was executed to investigated various cases of acceleration and deceleration
over a range of 70 g to 700 000g. The boundary layer profiles, boundary layer parameters and
skin friction coefficients were reported.
Three types of boundary layer responses to arbitrary motion were defined. Response Type I is viscous
dominant and mimics the steady state velocity profile. In Response Type II certain regions of the
boundary layer are dominated by viscosity and others by momentum. Response Type III is dominated
by momentum. In acceleration the near-wall velocity gradient increases with increasing acceleration. In
deceleration separation occurs at a result of momentum changes in the flow.
The mechanism that causes these responses have been identified using the developed boundary layer
equations. In acceleration the relative frame fictitious terms become a momentum source which results
in an increase in velocity gradient at the wall. In deceleration the relative frame fictitious terms become
a momentum sink that induced an adverse pressure gradient and subsequently laminar separation.